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lara [203]
3 years ago
8

A string is wrapped several times around the rim of a small hoop with radius 7cm and mass 2kg. The free end of the string is hel

d in place and the hoop is released from rest.
After the hoop has descended 80cm, calculate (a) the angular speed of the hoop and (b) the speed of its center.
Physics
1 answer:
Ivanshal [37]3 years ago
3 0

Answer:

Explanation:

Given that,

The radius of loop r = 7cm = 0.07m

Mass of hoop M = 2kg

The hoop is released from rest, the initial velocity is 0m/s

A. Angular speed of the hoop after a descended of h= 80cm = 0.8m

Applying the conservation of energy

Ei + W = Ef

Where,

Ei = initial energy of the system, I.e the initial potential and kinetic energy

Ef = final energy of the system I.e the final potential and kinetic energy

W = 0, since no external force is acting on the systems

Ui + K.Ei + 0 = Uf + K.Ef

System was initially at rest, K.Ei = 0

Uf = 0 at the zero level

Then,

Mgh = ½ •Icm•w² + ½M•Vcm²

Icm = Mr², since it is circular loop

Then,

Mgh = ½ •Mr²•w² + ½M•Vcm²

M cancels out

gh = ½ •r²•w² + ½ Vcm²

Since Vcm = wr

Then, gh = ½ •r²•w² + ½ w²r²

gh = r²w²

w = √(gh/r²)

w = √(9.81 × 0.8/0.07²)

w = 40 rad/s

b. Speed at the center

Since Vcm = wr

Vcm = 40×0.07

Vcm = 2.8 m/s

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An initially stationary object experiences an acceleration of 6 m/s2 for a time of 15 s. How far will it travel during that time
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Answer:

The object will travel 675 m during that time.

Explanation:

A body moves with constant acceleration motion or uniformly accelerated rectilinear motion (u.a.r.m) when the path is a straight line, but the velocity is not necessarily constant because there is an acceleration.

In other words, a body performs a u.a.r.m when its path is a straight line and its acceleration is constant. This implies that the speed increases or decreases uniformly.

In this case, the position is calculated using the expression:

x = xo + vo*t + ½*a*t²

where:

  • x0 is the initial position.
  • v0 is the initial velocity.
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  • t is the time interval in which the motion is studied.

In this case:

  • x0= 0
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  • t= 15 s

Replacing:

x= 0 + 0*15 s + ½*6 \frac{m}{s^{2} }*(15s)²

Solving:

x=½*6 \frac{m}{s^{2} }*(15s)²

x=½*6 \frac{m}{s^{2} }*225 s²

x= 675 m

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?/1 Jorge traveled 5 miles north to school. He then traveled 3 miles west to the store. Then he left the store and traveled 5 mi
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He's 3 miles west of school.

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Answer:

0.8712 m/s²

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We are given;

Velocity of first car; v1 = 33 m/s

Distance; d = 2.5 km = 2500 m

Acceleration of first car; a1 = 0 m/s² (constant acceleration)

Velocity of second car; v2 = 0 m/s (since the second car starts from rest)

From Newton's equation of motion, we know that;

d = ut + ½at²

Thus,for first car, we have;

d = v1•t + ½(a1)t²

Plugging in the relevant values, we have;

d = 33t + 0

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d = v2•t + ½(a2)•t²

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Since they meet at the next exit, then;

33t = ½(a2)t²

simplifying to get;

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Option (b) is correct.

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